Fitch and Intuitionistic Knowability

Percival, Philip

doi:10.2307/3328541

Cited by 67 publications

(3 citation statements)

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“…We are not, of course, the first to outline arguments that an intuitionistic conception of truth supports coreflection, see for instance Dean & Kurakawa (2009); Hart (1979); Khlentzos (2004); Murzi (2010); Percival (1990); Martino & Usberti (1994); Williamson (1982Williamson ( , 1988; Wright (1993a). 11 Our contention is that coreflection, when properly understood in line with the intended BHK semantics, is a fairly immediate consequence of uncontroversially intuitionistic views about truth, and should therefore be endorsed as foundational for a properly intuitionistic epistemology.…”

Section: Principles Of Intuitionistic Epistemic Logicmentioning

confidence: 99%

Intuitionistic Epistemic Logic

Artëmov

Protopopescu

2016

The Review of Symbolic Logic

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We outline an intuitionistic view of knowledge which maintains the original Brouwer-Heyting-Kolmogorov semantics for intuitionism and is consistent with the wellknown approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view co-reflection A → KA is valid and the factivity of knowledge holds in the form KA → ¬¬A 'known propositions cannot be false'.We show that the traditional form of factivity KA → A is a distinctly classical principle which, like tertium non datur A ∨ ¬A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA → A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.

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Section: Principles Of Intuitionistic Epistemic Logicmentioning

confidence: 99%

Intuitionistic Epistemic Logic

Artëmov

Protopopescu

2016

The Review of Symbolic Logic

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“…The deductive argument relies on classical logic. For a discussion of the Church-Fitch paradox against the background of intuitionistic logic, see (Williamson, 1982(Williamson, , 1988(Williamson, , 1992(Williamson, , 1994 and (Percival, 1990). Because of the transition from a thesis that is plausible to some to a conclusion that is implausible to all, the argument is seen by some as paradoxical.…”

Section: Every Truth Is Knowablementioning

confidence: 99%

Factive knowability and the problem of possible omniscience

Heylen

2018

Philos Stud

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Famously, the Church-Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In this article we will look closer at two proposals along these lines (Edgington 1985; Fuhrmann 2014a), because there are formal models available for each. It will be argued that, even though the problem of omniscience can be averted, the problem of possible or potential omniscience cannot: there is an accessible state at which all (actual) truths are known. Furthermore, it will be argued that possible or potential omniscience is a price that is too high to pay. Others who have proposed to solve the paradox with the help of a factive concept of knowability should take note (Fara 2010; Spencer 2017).Keywords Factive knowability; Actuality Potential knowledge; Knowability thesis; Church-Fitch paradox of knowability Possible omniscience Potential omniscience How to conceptualise knowability? In the philosophical literature the most common conceptualisation of knowability is in terms of having the possibility to know, i.e. there being an accessible possible world in which one knows. This * Earlier versions of this paper have been presented at the Leuven-Paris Analytic Workshop in Epistemology (Leuven, 19/01/2018), The Ninth Congress of Analytic Philosophy (Munich, 25/08/2017), and a CLAW Seminar (Leuven, 04/10/2016). I would like to thank all the audiences for their helpful feedback. In addition, I would like to thank Lorenz Demey and Davide Fassio for commenting on earlier versions of the paper. Last but not least, I would like to thank the two anonymous reviewers, who have given very detailed and extensive comments and suggestions for improvement.

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“…Percival (1990) argues that the intuitionistic revision of the paradox involves a further paradox stating that there are no necessary undecided statements, which seems absurd also from the verificationist perspective. Consider the assumption that there are undecided statements in the intuitionistic and epistemic calculus:…”

Section: Difficulties In the Intuitionistic Solution To The Knowabilimentioning

confidence: 99%

The Knowability Paradox in the Light of a Logic for Pragmatics

Carrara¹,

Chiffi

2014

Recent Trends in Philosophical Logic

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The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutionscalled logical revision -has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on socalled revisionary solutions to the paradox -solutions that put the blame on the underlying logic. Specifically, we analyse a possibile translation of the paradox into a modified intuitionistic fragment of a logic for pragmatics (KILP) inspired by Dalla Pozza and Garola in 1995. Our aim is to understand if KILP is a candidate for the logical revision of the paradox and to compare it with the standard intuitionistic solution to the paradox.

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Fitch and Intuitionistic Knowability

Cited by 67 publications

References 5 publications

Intuitionistic Epistemic Logic

Intuitionistic Epistemic Logic

Factive knowability and the problem of possible omniscience

The Knowability Paradox in the Light of a Logic for Pragmatics

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